二项分布极限近似的Python可视化仿真及教学应用

A Visual Simulation and Teaching Application Study of the Limit Approximation of the Binomial Distribution Based on Python

摘要: 二项分布的泊松近似和正态近似，是概率论与数理统计课的核心内容，能帮助学生更好地理解中心极限定理。本文用Python的scipy.stats和matplotlib库，做了二项分布与泊松、正态分布的叠加对比图，还实现了误差定量评估和动态收敛演示。通过典型参数的数值实验，验证了两种近似的有效性，分析了误差特点及适用条件，也检查了连续性校正对正态近似精度的改善。本文的可复现实验平台和可视化工具，有实际教学价值。

Abstract: The Poisson and normal approximations to the binomial distribution are key topics in probability and mathematical statistics courses, helping students grasp the central limit theorem better. This paper uses Python’s scipy.stats and matplotlib libraries to create overlaid comparison charts between the binomial distribution and its Poisson or normal counterparts, along with quantitative error assessment and dynamic convergence demos. Through numerical experiments with typical parameters, it verifies the effectiveness of both approximations, analyzes their error features and suitable conditions, and checks how continuity correction improves the normal approximation’s accuracy. The reproducible experiment platform and visualization tools here offer real value for teaching.